Nodal surfaces and interdimensional degeneracies

The aim of this paper is to shed light on the topology and properties of the nodes (i.e. the zeros of the wave function) in electronic systems. Using the "electrons on a sphere" model, we study the nodes of two-, three- and four-electron systems in various ferromagnetic configurations ($sp$, $p^2$, $sd$, $pd$, $p^3$, $sp^2$ and $sp^3$). In some particular cases ($sp$, $p^2$, $sd$, $pd$ and $p^3$), we rigorously prove that the non-interacting wave function has the same nodes as the exact (yet unknown) wave function. The number of atomic and molecular systems for which the exact nodes are known analytically is very limited and we show here that this peculiar feature can be attributed to interdimensional degeneracies. Although we have not been able to prove it rigorously, we conjecture that the nodes of the non-interacting wave function for the $sp^3$ configuration are exact.Comment: 7 pages, 3 figures, accepted for publication in the Journal of Chemical Physic

Positron Binding to Lithium Excited States

In the last 15 years hundreds of papers have been devoted to the study of positron-atom or positron-molecule interaction. A large body of evidence has accumulated showing that many atoms in their ground state can bind a positron forming an electronically stable system. Studies on the possibility that a positron binds to an atomic excited state, however, are scarce. The first atom that was proved able to bind a positron in its ground state is lithium. Surprisingly, nothing is known on the possibility that a positron could bind to one of its excited states. In this Letter we study the positron attachment to the 1s22p 2Po, 1s2s2p 2Po and 2p3 4So excited states of the lithium atom. While the 2Po state cannot bind a positron, and the 4So could at most form a metastable state, a positron can attach to the 4Po state of lithium forming a bound state with a binding energy of about 0.003 hartree. This state can alternatively be considered an excited state of the system e+Li and it could be, in principle, exploited in an experiment to detect e+Li, whose existence has been predicted theoretically but has not yet been observed experimentally

Stability and production of positron-diatomic molecule complexes

The energies at geometries close to the equilibrium for the e$^+$BeO and e$^+$LiF ground states were computed by means of diffusion Monte Carlo simulations. These results allow us to predict the equilibrium geometries and the vibrational frequencies for these exotic systems,and to discuss their stability with respect to the various dissociation channels. Since the adiabatic positron affinities were found to be smaller than the dissociation energies for both complexes, we propose these two molecules as possible candidates in the challenge to produce and detect stable positron-molecule systems.Comment: submitted to Phys. Rev. Let

Variance reduction in MCMC

We propose a general purpose variance reduction technique for MCMC estimators. The idea is obtained by combining standard variance reduction principles known for regular Monte Carlo simulations (Ripley, 1987) and the Zero-Variance principle introduced in the physics literature (Assaraf and Caffarel, 1999). The potential of the new idea is illustrated with some toy examples and an application to Bayesian estimationMarkov chain Monte carlo, Metropolis-Hastings algorithm, Variance reduction, Zero-Variance principle

Two positrons can form a chemical bond in (PsH)2

We show that two positrons can form a chemical bond between two otherwise repelling ions, similar to what happens to two hydrogen atoms forming a hydrogen molecule. Two positronium hydride atoms (PsH) can form the stable species (PsH)2 when the two coupled positrons have opposite spins, while they form an antibonding state if they have the same spin. This is completely analogous to the landmark description by Heitler and London [Z. Phys. 44, 455 (1927)] on the formation of a chemical bond in the hydrogen molecule coupling two electrons with opposite spins. This is the first time two positrons are shown to behave like two electrons in ordinary matter, enlarging the definition of what is a chemical bond dating back to Lewis [J. Am. Chem. Soc. 38, 762 (1916)]. We suggest a few experimental routes to form and detect such a peculiar molecule

Quantum Monte Carlo study of the H- impurity in small helium clusters

We report ground state energies and structural properties for small helium clusters (4He) containing an H- impurity computed by means of variational and diffusion Monte Carlo methods. Except for 4He_2H- that has a noticeable contribution from collinear geometries where the H- impurity lies between the two 4He atoms, our results show that our 4He_NH- clusters have a compact 4He_N subsystem that binds the H- impurity on its surface. The results for $N\geq 3$ can be interpreted invoking the different features of the minima of the He-He and He-H- interaction potentials.Comment: 12 pages, 7 Ps figure

Delayed Rejection Variational Monte Carlo

A new acceleration algorithm to address the problem of multiple time scales in variational Monte Carlo simulations is presented. Core electrons usually require smaller time steps than valence electrons. After a first attempted move has been rejected, the delayed rejection algorithm attempts a second move with a smaller time step, so moves of both valence and core electrons can be accepted. Results on Be and Ne atoms as test cases are presented. Correlation time and both average accepted displacement and acceptance ratio as a function of the distance from the nucleus evidence the efficiency of the proposed algorithm in dealing with the multiple time scales problem.